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Cross-impact and no-dynamic-arbitrage


  • M. Schneider
  • F. Lillo


We extend the ‘No-dynamic-arbitrage and market impact’-framework of Gatheral [Quant. Finance, 2010, 10(7), 749–759] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset i to asset j must be equal to the one from j to i. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.

Suggested Citation

  • M. Schneider & F. Lillo, 2019. "Cross-impact and no-dynamic-arbitrage," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 137-154, January.
  • Handle: RePEc:taf:quantf:v:19:y:2019:i:1:p:137-154
    DOI: 10.1080/14697688.2018.1467033

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    References listed on IDEAS

    1. Shanshan Wang & Thomas Guhr, 2016. "Microscopic Understanding of Cross-Responses between Stocks: a Two-Component Price Impact Model," Papers 1609.04890,, revised Jul 2017.
    2. Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    3. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    4. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
    5. Lee, Charles M C & Ready, Mark J, 1991. "Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-746, June.
    6. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
    7. Modena, Matteo & Linciano, Nadia & Gentile, Monica & Fancello, Francesco, 2014. "The liquidity of dual-listed corporate bonds: empirical evidence from Italian markets," MPRA Paper 62479, University Library of Munich, Germany, revised 23 Feb 2015.
    8. Schneider, Michael & Lillo, Fabrizio & Pelizzon, Loriana, 2016. "How has sovereign bond market liquidity changed? An illiquidity spillover analysis," SAFE Working Paper Series 151, Leibniz Institute for Financial Research SAFE.
    9. Zoltán Eisler & Jean-Philippe Bouchaud & Julien Kockelkoren, 2012. "The price impact of order book events: market orders, limit orders and cancellations," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1395-1419, September.
    10. Alfonso Dufour & Minh Nguyen, 2012. "Permanent trading impacts and bond yields," The European Journal of Finance, Taylor & Francis Journals, vol. 18(9), pages 841-864, October.
    11. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    12. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact," Papers 1602.02735,
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    Cited by:

    1. Alexander Barzykin & Fabrizio Lillo, 2019. "Optimal VWAP execution under transient price impact," Papers 1901.02327,, revised Jan 2019.
    2. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Papers 2004.01624,, revised Sep 2020.
    3. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    4. Francesco Cordoni & Fabrizio Lillo, 2020. "Instabilities in Multi-Asset and Multi-Agent Market Impact Games," Papers 2004.03546,, revised Dec 2020.
    5. Yi Li & Ju’e Guo & Kin Keung Lai & Jinzhao Shi, 0. "Optimal portfolio liquidation with cross-price impacts on trading," Operational Research, Springer, vol. 0, pages 1-20.
    6. L. C. Garcia Del Molino & I. Mastromatteo & Michael Benzaquen & J.-P. Bouchaud, 2019. "The Multivariate Kyle model: More is different," Working Papers hal-02323433, HAL.
    7. Samim Ghamami & Paul Glasserman, 2019. "Submodular Risk Allocation," Management Science, INFORMS, vol. 65(10), pages 4656-4675, October.
    8. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Papers 2102.02834,
    9. Seungki Min & Costis Maglaras & Ciamac C. Moallemi, 2018. "Cross-Sectional Variation of Intraday Liquidity, Cross-Impact, and their Effect on Portfolio Execution," Papers 1811.05524,
    10. Luis Carlos Garc'ia del Molino & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2018. "The Multivariate Kyle model: More is different," Papers 1806.07791,, revised Dec 2018.
    11. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Working Papers hal-02567489, HAL.
    12. Gerry Tsoukalas & Jiang Wang & Kay Giesecke, 2019. "Dynamic Portfolio Execution," Management Science, INFORMS, vol. 67(5), pages 2015-2040, May.

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